Casting shadows of clouds from HDR?
Yes, it is possible. An hdr environment texture is actually just like a sphere with a texture and emission shader assigned to it (kind of). And of course, you are standing in it. So if you have a solid black environment  texture (hdr or not), there will be no light in the rendered scene.

So to get shadows on the ground, you would have to have an environment texture with some darker areas that don't emmitt so much light. But I think that it would be easier to just put a plane that would cause a shadow where clouds are.

Something like this would do: